Condensazione di Bose-Einstein in trappole ottiche

Questo lavoro di tesi si occupa dello studio del fenomeno di condensazione di Bose-Einstein sia da un punto di vista teorico che, in maniera più accennata, da quello pratico-sperimentale; risulta pertanto strutturato in due parti. La prima è incentrata sull'analisi prettamente teorico-matematica dell'argomento, e si apre con l'introduzione dell'opportuno apparato formale atto alla trattazione della statistica quantistica; a tal proposito vengono definiti gli operatori di densità. Quindi viene affrontato il problema dell'indistinguibilità degli enti quantistici e del conseguente carattere di simmetria delle funzioni d'onda, individuando così la differenza tra particelle fermioniche e bosoniche. Di queste ultime vengono largamente studiate la statistica cui essere rispondono e le loro principali caratteristiche termodinamiche. Infine, viene analizzato il caso specifico del gas ideale di Bose, trattato nei limiti del continuo e termodinamico; è nel corso di questa trattazione che emerge il fenomeno di transizione chiamato condensazione di Bose-Einstein, di cui vengono ampiamente studiate le proprietà. La seconda parte, invece, è volta all'analisi delle tecniche sperimentali utilizzate per la realizzazione della condensazione, in particolare le trappole ottiche di dipolo; dopo averne studiato le caratteristiche, vengono illustrate alcune tecniche di raffreddamento di atomi intrappolati. Il lavoro si conclude con la trattazione delle principali tecniche diagnostiche e di riconoscimento del condensato.

Competition between boson condensation and molecule formation in 2D Bose-Fermi mixtures with a pairing interaction

The study of ultra-cold atomic gases is one of the most active field in contemporary physics. The main motivation for the interest in this field consists in the possibility to use ultracold gases to simulate in a controlled way quantum many-body systems of relevance to other fields of physics, or to create novel quantum systems with unusual physical properties. An example of the latter are Bose-Fermi mixtures with a tunable pairing interaction between bosons and fermions. In this work, we study with many-body diagrammatic methods the properties of this kind of mixture in two spatial dimensions, extending previous work for three dimensional Bose-Fermi mixtures. At zero temperature, we focus specifically on the competition between boson condensation and the pairing of bosons and fermions into molecules. By a numerical solution of the main equations resulting by our many-body diagrammatic formalism, we calculate and present results for several thermodynamic quantities of interest. Differences and similarities between the two-dimensional and three-dimensional cases are pointed out. Finally, our new results are applied to discuss a recent proposal for creating a p-wave superfluid in Bose-Fermi mixtures with the fermionic molecules which form for sufficiently strong Bose-Fermi attraction.

Ultracold Bose-Fermi mixtures with pairing: quantum phase transition, mechanical stability, and trap confinement

Ultracold dilute gases occupy an important role in modern physics and they are employed to verify fundamental quantum theories in most branches of theoretical physics. The scope of this thesis work is the study of Bose-Fermi (BF) mixtures at zero temperature with a tunable pairing between bosons and fermions. The mixtures are treated with diagrammatic quantum many-body methods based on the so-called T-matrix formalism. Starting from the Fermi-polaron limit, I will explore various values of relative concentrations up to mixtures with a majority of bosons, a case barely considered in previous works. An unexpected quantum phase transition is found to occur in a certain range of BF coupling for mixture with a slight majority of bosons. The mechanical stability of mixtures has been analysed, when the boson-fermion interaction is changed from weak to strong values, in the light of experimental results recently obtained for a double-degenerate Bose-Fermi mixture of 23 Na - 40 K. A possible improvement in the description of the boson-boson repulsion based on Popov's theory is proposed. Finally, the effects of a harmonic trapping potential are described, with a comparison with the experimental data for the condensate fraction recently obtained for a trapped 23 Na - 40 K mixture.

Spectral properties of resonant Bose-Fermi mixtures

The object of study of the present work are Bose-Fermi mixtures in three dimensions at zero temperature. The system is characterized by a great tunability of physical parameters that is achieved by means of a Fano-Feshbach resonance. As a result, there are mainly two regimes: we move from a situation in which bosons and fermions are weakly interacting to a context in which bosons are coupled to fermions so as to form molecules that are composite fermions, as the coupling between the two types of particles is increased. In the former case, we can describe the mixture as a weakly attractive Bose-Fermi one, while in the latter the same is described in terms of molecules and excess atoms or particles which are unpaired. The main aim of the thesis is to analyze the spectral weight functions which represent the single-particle excitation spectra of the system and are relevant to recent radio-frequency spectroscopy experiments of the system. In order to pursue this objective, diagrammatic methods are used. The formalism is developed within the T-matrix approach: it consists of an approximate calculation whichselects exclusively the class of Feynman’s diagrams that collects all possible repeated boson-fermion interaction.